多群伴随中子通量积分方程的一种Monte Carlo新解法

伴随Monte Carlo方法对计算点通量、辐射环境问题等有其独特的优越性,迄今为止是别的方法所不具备的,但伴随Monte Carlo方法所给出的估计的方差常常是比较大的。本文对多群伴随通量积分方程给出一种降低方差的Monte Carlo解法——"最佳"权重变化因子法。计算结果表明,这种方法可使方差明显减小。     

随机参激和外激联合作用下非线性动力系统的路径积分解

将基于Gauss Legendre公式的路径积分法推广到随机参激和外激联合作用的非线性动力系统.研究了受高斯白噪声参激和外激联合作用的非线性振子，将所得路径积分解与其精确解（满足一定条件时该系统存在精确解）或Monte Carlo随机模拟结果相比较，充分验证了路径积分的准确性.并借助路径积分数值解，捕捉到该随机系统的一维P分岔. 关键词： 路径积分 P分岔 随机参激 随机外激     

2维O(3)非线性σ模型的解析研究

在格点规范理论中应用变分累积展开方法,解析计算了2维O(3)非线性σ模型的内能和比热,并将计算结果和Monte Carlo数据进行了比较.     

激光放大器腔光传输的并行模拟计算

Monte—Carlo方法是一种建立在数理统计基础上的统计实验方法，它主要用在很难建立数学模型的复杂随机系统方面，如经常用于处理热辐射问题等。在计算求解激光片状放大器腔的光传输问题时，对灯所发出的光，不仅需要考虑到光线发出的具体位置，而且还需要考虑到光线发出的具体方向，即这是一个两重的积分问题，其离散化处理明显属于一种大量独立的、重复性的实验，极适合于使用Monte—Carlo方法。     

基于Monte Carlo的热脉冲法数据分析

热脉冲法是测量聚合物介质薄膜空间电荷分布的有效方法之一, 其数据的分析涉及第一类Fredholm积分方程, 只能采用合适的数值计算方法进行求解, 而Monte Carlo法是近年来提出的数值求解该方程的方法之一. 本文尝试使用Monte Carlo法在频域内实现热脉冲数据的分析, 通过一系列模拟计算讨论Monte Carlo法的分析效果. 计算结果表明: Monte Carlo法可实现对热脉冲法实验数据的有效分析, 提取被测薄膜内的电场分布, 而且计算的电场分布在整个样品厚度上都与真实分布较好地符合, 可有效地弥补尺度变换法只在样品表面附近获得较高准确度的缺陷. 该方法的局限性在于计算结果存在一定的振荡, 且在噪声和数据误差的影响下, 其准确性很大程度上依赖于奇异值分解过程中容差的选择, 在应用的方便程度方面还有待进一步提升.     

变分累积展开方法中确定相变点的新方法

在计算有限温度SU(2)格点规范模型Polyakov线的过程中,考虑到变分累积展开法中有限距离相互作用效应与Monte Carlo中的有限体积效应的相似性,采用了新的方法来确定相变点.与已有的方法以及Monte Carlo模拟给出的结果比较,新方法给出的结果更接近Monte Carlo结果.     

~(60)Co和高能电子在硅中NIEL的Monte Carlo计算

本文提出了计算高能电子和 非电离能量损失 (NIEL)的 Monte Carlo方法 ,首次利用 Monte Carlo方法计算了高能电子和 6 0 Co 的 NIEL.给出了电子和 6 0 Co 在半导体硅材料中产生的 NIEL和缺陷分布 .计算结果与文献的比较表明模型是合理的 .     

Monte Carlo方法模拟非直视紫外光散射覆盖范围

针对大气中紫外光散射通信的特点, 用Monte Carlo方法对紫外光非直视(NLOS) 通信三种工作方式的覆盖范围进行分析, 建立了基于Monte Carlo方法的NLOS紫外光传输模型.利用Monte Carlo模拟方法对三种NLOS散射方式的单次和多次散射路径损耗及覆盖范围进行模拟研究, 结果表明, 多次散射和单次散射的路径损耗基本一致, NLOS(a) 类全向发送全向接收通信方式覆盖范围最小但全方位性好, NLOS(b) 类定向发送全向接收通信方式的覆盖范围较大但有一定方向性, NLOS(c) 类定向发送定向接收通信方式的覆盖范围最大但有很强的方向性.     

Monte Carlo方法在单粒子翻转数值模拟中的应用

描述了在单粒子翻转数值模拟中的一种有效方法-Monte Carlo方法,并对该方法中的粒子输运过程和相关的随机抽样进行了描述.对14MeV的中子从存储器硅片表面随机入射引起的单粒子翻转进行了计算和分析,同时计算了Monte Carlo方法引起的误差.     

巨正则量子Monte Carlo方法和二维Hubbard模型的研究

用巨正则量子Monte Carlo方法,计算了二维单带Hubbard模型的局域磁矩、磁化率、交错磁化率和内能等物理量.结果表明,用巨正则量子Monte Carlo方法能够统一地研究Hubbard模型的关联强度从弱至强区域的性质,它是处理强关联多体系统的有效方法.     

Monte Carlo simulation in the theory of wave propagation in random media: I. Modified and Feynman path integrals

The purpose of this article (comprising parts I and II) is to develop and test the approach of combining a path-integral technique and a complex-valued Monte Carlo method to calculate the highest moments of the Green function of the stochastic wave equation for a random medium against the background of large-scale inhomogeneities. In part I, the new modified path-integral representations of the Green function moments of the stochastic wave equation have been developed. The limiting transition of these representations to the Feynman path integrals corresponding to the parabolic approximation is discussed. Path-integral representations for Green function moments are given for three models: a model of the stochastic wave equation and models of parabolic and Markov approximations. The Metropolis algorithm underlying the Monte Carlo method for calculating real and complex-valued path integrals is discussed in brief. Numerical results are presented in part II of the article.     

High-density phenomena in hydrogen plasma

A novel path-integral representation of the many-particle density operator is presented which makes direct Fermionic path-integral Monte Carlo simulations feasible over a wide range of parameters. The method is applied to compute the pressure, energy, and pair distribution functions of a hydrogen plasma in the region of strong coupling and strong degeneracy. Our numerical results allow one to analyze the atom and molecule formation and breakup and predict, at high density, proton ordering and pairing of electrons.     

Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model

Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations.     

Study of electron solvation in polar solvents using path integral calculations

A path-integral Monte Carlo algorithm for the simulation of electrons solvated in polar liquids is briefly outlined, and results are presented for the electron solvated in liquid water.     

Reentrant behavior of the phase stiffness in Josephson junction arrays

The phase diagram of a 2D Josephson junction array with large substrate resistance, described by a quantum XY model, is studied by means of Fourier path-integral Monte Carlo. A genuine Berezinskii-Kosterlitz-Thouless transition is found up to a threshold value g( small star, filled ) of the quantum coupling, beyond which no phase coherence is established. Slightly below g( small star, filled ) the phase stiffness shows a reentrant behavior with temperature, in connection with a low-temperature disappearance of the superconducting phase, driven by strong nonlinear quantum fluctuations.     

A diffusion Monte Carlo study of small para-hydrogen clusters

An improved Monte Carlo diffusion model is used to calculate the ground state energies and chemical potentials of parahydrogen clusters of three to forty molecules, using two different p-H₂-p-H₂ interactions. The improvement is due to three-body correlations in the importance sampling, to the time step adjustment and to a better estimation of statistical errors. In contrast to path-integral Monte Carlo results, this method predicts no magic clusters other than that with thirteen molecules.      

Monte Carlo Study of Localization on a One-Dimensional Lattice

We study the equilibrium properties of a single quantum particle interacting with a classical lattice gas. We develop a path-integral formalism in which the quantum particle is represented by a closed, variable-step random walk on the lattice. After demonstrating that a Metropolis algorithm correctly predicts the properties of a free particle, we extend it to investigate the behavior of the quantum particle interacting with the lattice gas. Evidence of weak localization is observed under conditions of quenched disorder, while self-trapping clearly occurs for the fully annealed system. Compared with continuous space systems, convergence of Monte Carlo simulations in this minimum model is orders of magnitude faster in cpu time. Therefore the system behavior can be investigated for a much larger domain of thermodynamic parameters (e.g., density and temperature) in a reasonable time.     

Electron wave packets: Quantum statistics in path integral representation

Fundamental relations between ensemble-averaged kinetic energy, pressure, and virial are obtained for quantum many-particle systems at finite temperatures. A path-integral method is developed for calculating kinetic energy for mixed (quantum-classical) systems. The method eliminates the problem of divergent variance. Path-integral Monte Carlo simulations are performed to validate the method as applied to single-electron and electron-pair wave packets, with exact treatment of exchange symmetry and spin states. Quantitative results are compared with corresponding characteristics calculated for point charges.     

Monte Carlo simulation of quantum statistical lattice models

In this article we review recent developments in computational methods for quantum statistical lattice problems. We begin by giving the necessary mathematical basis, the generalized Trotter formula, and discuss the computational tools, exact summations and Monte Carlo simulation, that will be used to examine explicit examples. To illustrate the general strategy, the method is applied to an analytically solvable, non-trivial, model: the one-dimensional Ising model in a transverse field. Next it is shown how to generalized Trotter formula most naturally leads to different path-integral representations of the partition function by considering one-dimensional fermion lattice models. We show how to analyze the different representations and discuss Monte Carlo simulation results for one-dimensional fermions. Then Monte Carlo work on one- and two-dimensional spin-$\text{1}\text{2}$ models based upon the Trotter formula approach is reviewed and the more dedicated Handscomb Monte Carlo method is discussed. We consider electron-phonon models and discuss Monte Carlo simulation data on the Molecular Crystal Model in one, two and three dimensions and related one-dimensional polaron models. Exact numerical results are presented for free fermions and free bosons in the canonical ensemble. We address the main problem of Monte Carlo simulations of fermions in more than one dimension: the cancellation of large contributions. Free bosons on a lattice are compared with bosons in a box and the effects of finite size on Bose-Einstein condensation are discussed.     

A dynamical mean field theory for the study of surface diffusion constants

We present a combined analytical and numerical approach based on the Mori projection operator formalism and Monte Carlo simulations to study surface diffusion within the lattice-gas model. In the present theory, the average jump rate and the susceptibility factor appearing are evaluated through Monte Carlo simulations, while the memory functions are approximated by the known results for a Langmuir gas model. This leads to a dynamical mean field theory (DMF) for collective diffusion, while approximate correlation effects beyond DMF are included for tracer diffusion. We apply our formalism to three very different strongly interacting systems and compare the results of the new approach with those of usual Monte Carlo simulations. We find that the combined approach works very well for collective diffusion, whereas for tracer diffusion the influence of interactions on the memory effects is more prominent.